{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bayesian Parametric Survival Analysis with PyMC3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running on PyMC3 v3.6\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "from matplotlib import pyplot as plt\n",
    "from matplotlib.ticker import StrMethodFormatter\n",
    "import numpy as np\n",
    "import pymc3 as pm\n",
    "import scipy as sp\n",
    "import seaborn as sns\n",
    "from statsmodels import datasets\n",
    "from theano import shared, tensor as tt\n",
    "\n",
    "plt.style.use('seaborn-darkgrid')\n",
    "print('Running on PyMC3 v{}'.format(pm.__version__))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Survival analysis](https://en.wikipedia.org/wiki/Survival_analysis) studies the distribution of the time between when a subject comes under observation and when that subject experiences an event of interest.  One of the fundamental challenges of survival analysis (which also makes is mathematically interesting) is that, in general, not every subject will experience the event of interest before we conduct our analysis.  In more concrete terms, if we are studying the time between cancer treatment and death (as we will in this post), we will often want to analyze our data before every subject has died.  This phenomenon is called <a href=\"https://en.wikipedia.org/wiki/Censoring_(statistics)\">censoring</a> and is fundamental to survival analysis.\n",
    "\n",
    "I have previously [written](http://austinrochford.com/posts/2015-10-05-bayes-survival.html) about Bayesian survival analysis using the [semiparametric](https://en.wikipedia.org/wiki/Semiparametric_model) [Cox proportional hazards model](https://en.wikipedia.org/wiki/Proportional_hazards_model#The_Cox_model).  Implementing that semiparametric model in PyMC3 involved some fairly complex `numpy` code and nonobvious probability theory equivalences.  This post illustrates a parametric approach to Bayesian survival analysis in PyMC3.  Parametric models of survival are simpler to both implement and understand than semiparametric models; statistically, they are also more [powerful](https://en.wikipedia.org/wiki/Statistical_power) than non- or semiparametric methods _when they are correctly specified_. This post will not further cover the differences between parametric and nonparametric models or the various methods for chosing between them.\n",
    "\n",
    "As in the previous post, we will analyze [mastectomy data](https://vincentarelbundock.github.io/Rdatasets/doc/HSAUR/mastectomy.html) from `R`'s [`HSAUR`](https://cran.r-project.org/web/packages/HSAUR/index.html) package.  First, we load the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "sns.set()\n",
    "blue, green, red, purple, gold, teal = sns.color_palette(n_colors=6)\n",
    "\n",
    "pct_formatter = StrMethodFormatter('{x:.1%}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = (datasets.get_rdataset('mastectomy', 'HSAUR', cache=True)\n",
    "              .data\n",
    "              .assign(metastized=lambda df: 1. * (df.metastized == \"yes\"),\n",
    "                      event=lambda df: 1. * df.event))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>time</th>\n",
       "      <th>event</th>\n",
       "      <th>metastized</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>23</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>47</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>69</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>70</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>100</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   time  event  metastized\n",
       "0    23    1.0         0.0\n",
       "1    47    1.0         0.0\n",
       "2    69    1.0         0.0\n",
       "3    70    0.0         0.0\n",
       "4   100    0.0         0.0"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The column `time` represents the survival time for a breast cancer patient after a mastectomy, measured in months.  The column `event` indicates whether or not the observation is censored.  If `event` is one, the patient's death was observed during the study; if `event` is zero,  the patient lived past the end of the study and their survival time is censored.  The column `metastized` indicates whether the cancer had [metastized](https://en.wikipedia.org/wiki/Metastasis) prior to the mastectomy.  In this post, we will use Bayesian parametric survival regression to quantify the difference in survival times for patients whose cancer had and had not metastized."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Accelerated failure time models\n",
    "\n",
    "[Accelerated failure time models](https://en.wikipedia.org/wiki/Accelerated_failure_time_model) are the most common type of parametric survival regression models.  The fundamental quantity of survival analysis is the [survival function](https://en.wikipedia.org/wiki/Survival_function); if $T$ is the random variable representing the time to the event in question, the survival function is $S(t) = P(T > t)$.  Accelerated failure time models incorporate covariates $\\mathbf{x}$ into the survival function as\n",
    "\n",
    "$$S(t\\ |\\ \\beta, \\mathbf{x}) = S_0\\left(\\exp\\left(\\beta^{\\top} \\mathbf{x}\\right) \\cdot t\\right),$$\n",
    "\n",
    "where $S_0(t)$ is a fixed baseline survival function.  These models are called \"accelerated failure time\" because, when $\\beta^{\\top} \\mathbf{x} > 0$, $\\exp\\left(\\beta^{\\top} \\mathbf{x}\\right) \\cdot t > t$, so the effect of the covariates is to accelerate the _effective_ passage of time for the individual in question.  The following plot illustrates this phenomenon using an exponential survival function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "S0 = sp.stats.expon.sf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "t = np.linspace(0, 10, 100)\n",
    "\n",
    "ax.plot(t, S0(5 * t),\n",
    "        label=r\"$\\beta^{\\top} \\mathbf{x} = \\log\\ 5$\");\n",
    "ax.plot(t, S0(2 * t),\n",
    "        label=r\"$\\beta^{\\top} \\mathbf{x} = \\log\\ 2$\");\n",
    "ax.plot(t, S0(t),\n",
    "        label=r\"$\\beta^{\\top} \\mathbf{x} = 0$ ($S_0$)\");\n",
    "ax.plot(t, S0(0.5 * t),\n",
    "        label=r\"$\\beta^{\\top} \\mathbf{x} = -\\log\\ 2$\");\n",
    "ax.plot(t, S0(0.2 * t),\n",
    "        label=r\"$\\beta^{\\top} \\mathbf{x} = -\\log\\ 5$\");\n",
    "\n",
    "ax.set_xlim(0, 10);\n",
    "ax.set_xlabel(r\"$t$\");\n",
    "\n",
    "ax.yaxis.set_major_formatter(pct_formatter);\n",
    "ax.set_ylim(-0.025, 1);\n",
    "ax.set_ylabel(r\"Survival probability, $S(t\\ |\\ \\beta, \\mathbf{x})$\");\n",
    "\n",
    "ax.legend(loc=1);\n",
    "ax.set_title(\"Accelerated failure times\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Accelerated failure time models are equivalent to log-linear models for $T$,\n",
    "\n",
    "$$Y = \\log T = \\beta^{\\top} \\mathbf{x} + \\varepsilon.$$\n",
    "\n",
    "A choice of distribution for the error term $\\varepsilon$ determines baseline survival function, $S_0$, of the accelerated failure time model.  The following table shows the correspondence between the distribution of $\\varepsilon$ and $S_0$ for several common accelerated failure time models.\n",
    "\n",
    "<center>\n",
    "<table border=\"1\">\n",
    "    <tr>\n",
    "        <th>Log-linear error distribution ($\\varepsilon$)</th>\n",
    "        <th>Baseline survival function ($S_0$)</th>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>[Normal](https://en.wikipedia.org/wiki/Normal_distribution)</td>\n",
    "        <td>[Log-normal](https://en.wikipedia.org/wiki/Log-normal_distribution)</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>Extreme value ([Gumbel](https://en.wikipedia.org/wiki/Gumbel_distribution))</td>\n",
    "        <td>[Weibull](https://en.wikipedia.org/wiki/Weibull_distribution)</td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>[Logistic](https://en.wikipedia.org/wiki/Logistic_distribution)</td>\n",
    "        <td>[Log-logistic](https://en.wikipedia.org/wiki/Log-logistic_distribution)</td>\n",
    "    </tr>\n",
    "</table>\n",
    "</center>\n",
    "\n",
    "Accelerated failure time models are conventionally named after their baseline survival function, $S_0$.  The rest of this post will show how to implement Weibull and log-logistic survival regression models in PyMC3 using the mastectomy data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Weibull survival regression\n",
    "\n",
    "In this example, the covariates are $\\mathbf{x}_i = \\left(1\\ x^{\\textrm{met}}_i\\right)^{\\top}$, where\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "x^{\\textrm{met}}_i\n",
    "    & = \\begin{cases}\n",
    "        0 & \\textrm{if the } i\\textrm{-th patient's cancer had not metastized} \\\\\n",
    "        1 & \\textrm{if the } i\\textrm{-th patient's cancer had metastized}\n",
    "    \\end{cases}.\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "We construct the matrix of covariates $\\mathbf{X}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_patient, _ = df.shape\n",
    "\n",
    "X = np.empty((n_patient, 2))\n",
    "X[:, 0] = 1.\n",
    "X[:, 1] = df.metastized"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We place independent, vague normal prior distributions on the regression coefficients,\n",
    "\n",
    "$$\\beta \\sim N(0, 5^2 I_2).$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "VAGUE_PRIOR_SD = 5."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "with pm.Model() as weibull_model:\n",
    "    β = pm.Normal('β', 0., VAGUE_PRIOR_SD, shape=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The covariates, $\\mathbf{x}$, affect value of $Y = \\log T$ through $\\eta = \\beta^{\\top} \\mathbf{x}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_ = shared(X)\n",
    "\n",
    "with weibull_model:\n",
    "    η = β.dot(X_.T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For Weibull regression, we use\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "    \\varepsilon\n",
    "        & \\sim \\textrm{Gumbel}(0, s) \\\\\n",
    "    s\n",
    "        & \\sim \\textrm{HalfNormal(5)}.\n",
    "\\end{align*}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "with weibull_model:\n",
    "    s = pm.HalfNormal('s', 5.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are nearly ready to specify the likelihood of the observations given these priors.  Before doing so, we transform the observed times to the log scale and standardize them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = np.log(df.time.values)\n",
    "y_std = (y - y.mean()) / y.std()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The likelihood of the data is specified in two parts, one for uncensored samples, and one for censored samples.  Since $Y = \\eta + \\varepsilon$, and $\\varepsilon \\sim \\textrm{Gumbel}(0, s)$, $Y \\sim \\textrm{Gumbel}(\\eta, s)$.  For the uncensored survival times, the likelihood is implemented as"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "cens = df.event.values == 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/canyon/miniconda3/envs/pymc/lib/python3.7/site-packages/theano/tensor/subtensor.py:2197: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  rval = inputs[0].__getitem__(inputs[1:])\n"
     ]
    }
   ],
   "source": [
    "cens_ = shared(cens)\n",
    "\n",
    "with weibull_model:\n",
    "    y_obs = pm.Gumbel(\n",
    "        'y_obs', η[~cens_], s,\n",
    "        observed=y_std[~cens]\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For censored observations, we only know that their true survival time exceeded the total time that they were under observation.  This probability is given by the survival function of the Gumbel distribution,\n",
    "\n",
    "$$P(Y \\geq y) = 1 - \\exp\\left(-\\exp\\left(-\\frac{y - \\mu}{s}\\right)\\right).$$\n",
    "\n",
    "This survival function is implemented below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gumbel_sf(y, μ, σ):\n",
    "    return 1. - tt.exp(-tt.exp(-(y - μ) / σ))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now specify the likelihood for the censored observations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "with weibull_model:\n",
    "    y_cens = pm.Potential(\n",
    "        'y_cens', gumbel_sf(y_std[cens], η[cens_], s)\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now sample from the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "SEED = 845199 # from random.org, for reproducibility\n",
    "\n",
    "SAMPLE_KWARGS = {\n",
    "    'chains': 3,\n",
    "    'tune': 1000,\n",
    "    'random_seed': [\n",
    "        SEED,\n",
    "        SEED + 1,\n",
    "        SEED + 2\n",
    "    ]\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (3 chains in 4 jobs)\n",
      "NUTS: [s, β]\n",
      "Sampling 3 chains: 100%|██████████| 4500/4500 [00:02<00:00, 1958.11draws/s]\n"
     ]
    }
   ],
   "source": [
    "with weibull_model:\n",
    "    weibull_trace = pm.sample(**SAMPLE_KWARGS)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The energy plot and Bayesian fraction of missing information give no cause for concern about poor mixing in NUTS."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/canyon/miniconda3/envs/pymc/lib/python3.7/site-packages/arviz/data/io_pymc3.py:56: FutureWarning: arrays to stack must be passed as a \"sequence\" type such as list or tuple. Support for non-sequence iterables such as generators is deprecated as of NumPy 1.16 and will raise an error in the future.\n",
      "  chain_likelihoods.append(np.stack(log_like))\n",
      "/home/canyon/miniconda3/envs/pymc/lib/python3.7/site-packages/theano/tensor/subtensor.py:2197: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  rval = inputs[0].__getitem__(inputs[1:])\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.energyplot(weibull_trace);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0932276551919557"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pm.bfmi(weibull_trace)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Gelman-Rubin statistics also indicate convergence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0020687081561328"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max(np.max(gr_stats) for gr_stats in pm.rhat(weibull_trace).values())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below we plot posterior distributions of the parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1490.4x331.2 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.plot_posterior(weibull_trace, lw=0, alpha=0.5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These are somewhat interesting (espescially the fact that the posterior of $\\beta_1$ is fairly well-separated from zero), but the posterior predictive survival curves will be much more interpretable.\n",
    "\n",
    "The advantage of using [`theano.shared`](http://deeplearning.net/software/theano_versions/dev/library/compile/shared.html) variables is that we can now change their values to perform posterior predictive sampling.  For posterior prediction, we set $X$ to have two rows, one for a subject whose cancer had not metastized and one for a subject whose cancer had metastized.  Since we want to predict actual survival times, none of the posterior predictive rows are censored."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_pp = np.empty((2, 2))\n",
    "X_pp[:, 0] = 1.\n",
    "X_pp[:, 1] = [0, 1]\n",
    "X_.set_value(X_pp)\n",
    "\n",
    "cens_pp = np.repeat(False, 2)\n",
    "cens_.set_value(cens_pp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1500/1500 [00:00<00:00, 2305.66it/s]\n"
     ]
    }
   ],
   "source": [
    "with weibull_model:\n",
    "    pp_weibull_trace = pm.sample_posterior_predictive(\n",
    "        weibull_trace, samples=1500, vars=[y_obs]\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The posterior predictive survival times show that, on average, patients whose cancer had not metastized survived longer than those whose cancer had metastized."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "t_plot = np.linspace(0, 230, 100)\n",
    "\n",
    "weibull_pp_surv = (np.greater_equal\n",
    "                     .outer(np.exp(y.mean() + y.std() * pp_weibull_trace['y_obs']),\n",
    "                            t_plot))\n",
    "weibull_pp_surv_mean = weibull_pp_surv.mean(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "\n",
    "ax.plot(t_plot, weibull_pp_surv_mean[0],\n",
    "        c=blue, label=\"Not metastized\");\n",
    "ax.plot(t_plot, weibull_pp_surv_mean[1],\n",
    "        c=red, label=\"Metastized\");\n",
    "\n",
    "ax.set_xlim(0, 230);\n",
    "ax.set_xlabel(\"Weeks since mastectomy\");\n",
    "\n",
    "ax.set_ylim(top=1);\n",
    "ax.yaxis.set_major_formatter(pct_formatter);\n",
    "ax.set_ylabel(\"Survival probability\");\n",
    "\n",
    "ax.legend(loc=1);\n",
    "ax.set_title(\"Weibull survival regression model\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Log-logistic survival regression\n",
    "\n",
    "Other accelerated failure time models can be specificed in a modular way by changing the prior distribution on $\\varepsilon$.  A log-logistic model corresponds to a [logistic](https://en.wikipedia.org/wiki/Logistic_distribution) prior on $\\varepsilon$.  Most of the model specification is the same as for the Weibull model above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_.set_value(X)\n",
    "cens_.set_value(cens)\n",
    "\n",
    "with pm.Model() as log_logistic_model:\n",
    "    β = pm.Normal('β', 0., VAGUE_PRIOR_SD, shape=2)\n",
    "    η = β.dot(X_.T)\n",
    "    \n",
    "    s = pm.HalfNormal('s', 5.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use the prior $\\varepsilon \\sim \\textrm{Logistic}(0, s)$.  The survival function of the logistic distribution is\n",
    "\n",
    "$$P(Y \\geq y) = 1 - \\frac{1}{1 + \\exp\\left(-\\left(\\frac{y - \\mu}{s}\\right)\\right)},$$\n",
    "\n",
    "so we get the likelihood "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "def logistic_sf(y, μ, s):\n",
    "    return 1. - pm.math.sigmoid((y - μ) / s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/canyon/miniconda3/envs/pymc/lib/python3.7/site-packages/theano/tensor/subtensor.py:2197: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  rval = inputs[0].__getitem__(inputs[1:])\n"
     ]
    }
   ],
   "source": [
    "with log_logistic_model:\n",
    "    y_obs = pm.Logistic(\n",
    "        'y_obs', η[~cens_], s,\n",
    "        observed=y_std[~cens]\n",
    "    )\n",
    "    y_cens = pm.Potential(\n",
    "        'y_cens', logistic_sf(y_std[cens], η[cens_], s)\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now sample from the log-logistic model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "/home/canyon/miniconda3/envs/pymc/lib/python3.7/site-packages/theano/tensor/subtensor.py:2197: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  rval = inputs[0].__getitem__(inputs[1:])\n",
      "Multiprocess sampling (3 chains in 4 jobs)\n",
      "NUTS: [s, β]\n",
      "Sampling 3 chains: 100%|██████████| 4500/4500 [00:02<00:00, 1965.00draws/s]\n",
      "The number of effective samples is smaller than 25% for some parameters.\n"
     ]
    }
   ],
   "source": [
    "with log_logistic_model:\n",
    "    log_logistic_trace = pm.sample(**SAMPLE_KWARGS)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All of the sampling diagnostics look good for this model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/canyon/miniconda3/envs/pymc/lib/python3.7/site-packages/arviz/data/io_pymc3.py:56: FutureWarning: arrays to stack must be passed as a \"sequence\" type such as list or tuple. Support for non-sequence iterables such as generators is deprecated as of NumPy 1.16 and will raise an error in the future.\n",
      "  chain_likelihoods.append(np.stack(log_like))\n",
      "/home/canyon/miniconda3/envs/pymc/lib/python3.7/site-packages/theano/tensor/subtensor.py:2197: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  rval = inputs[0].__getitem__(inputs[1:])\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.energyplot(log_logistic_trace);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.003922322462184"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pm.bfmi(log_logistic_trace)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9995156092420677"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max(np.max(gr_stats) for gr_stats in pm.rhat(log_logistic_trace).values())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, we calculate the posterior expected survival functions for this model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1500/1500 [00:00<00:00, 2423.11it/s]\n"
     ]
    }
   ],
   "source": [
    "X_.set_value(X_pp)\n",
    "cens_.set_value(cens_pp)\n",
    "\n",
    "with log_logistic_model:\n",
    "    pp_log_logistic_trace = pm.sample_posterior_predictive(\n",
    "        log_logistic_trace, samples=1500, vars=[y_obs]\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "log_logistic_pp_surv = (np.greater_equal\n",
    "                          .outer(np.exp(y.mean() + y.std() * pp_log_logistic_trace['y_obs']),\n",
    "                                 t_plot))\n",
    "log_logistic_pp_surv_mean = log_logistic_pp_surv.mean(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "ax.plot(t_plot, weibull_pp_surv_mean[0],\n",
    "        c=blue, label=\"Weibull, not metastized\");\n",
    "ax.plot(t_plot, weibull_pp_surv_mean[1],\n",
    "        c=red, label=\"Weibull, metastized\");\n",
    "\n",
    "ax.plot(t_plot, log_logistic_pp_surv_mean[0],\n",
    "        '--', c=blue, \n",
    "        label=\"Log-logistic, not metastized\");\n",
    "ax.plot(t_plot, log_logistic_pp_surv_mean[1],\n",
    "        '--', c=red,\n",
    "        label=\"Log-logistic, metastized\");\n",
    "\n",
    "ax.set_xlim(0, 230);\n",
    "ax.set_xlabel(\"Weeks since mastectomy\");\n",
    "\n",
    "ax.set_ylim(top=1);\n",
    "ax.yaxis.set_major_formatter(pct_formatter);\n",
    "ax.set_ylabel(\"Survival probability\");\n",
    "\n",
    "ax.legend(loc=1);\n",
    "ax.set_title(\"Weibull and log-logistic\\nsurvival regression models\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This post has been a short introduction to implementing parametric survival regression models in PyMC3 with a fairly simple data set.  The modular nature of probabilistic programming with PyMC3 should make it straightforward to generalize these techniques to more complex and interesting data set."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Authors\n",
    "\n",
    "- Originally authored as a blog post by [Austin Rochford](https://austinrochford.com/posts/2017-10-02-bayes-param-survival.html) on October 2, 2017.\n",
    "- Updated by [George Ho](https://eigenfoo.xyz/) on July 18, 2018."
   ]
  }
 ],
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